Liquidity Depletion, Long-Memory Order Flow, and Square-Root Impact

Summary

This document presents a dynamical theory linking order flow, market liquidity, and price impact. Under mild assumptions about order flow and approximately diffusive prices, the theory predicts a V-shaped average supply and demand profile that becomes very thin near the current price. Large orders therefore need to be split into smaller trades to pass through the available liquidity, which helps explain persistent patterns in trade direction.

The same scarcity of nearby liquidity can make small trades move prices disproportionately, producing a nonlinear response consistent with the square-root impact law. The document says it provides additional empirical support for that law and tests the proposed mechanism with a numerical order-flow model built from the theory’s basic ingredients. The supplied abstract does not describe the data, model specifications, or quantitative results, so it offers a conceptual account rather than enough detail to assess the empirical evidence or apply the model directly.

Key ideas

• The theory predicts that average supply and demand thin out near the current price.
• Fragmenting large orders helps them pass through available liquidity and can create long-memory in trade signs.
• Low local liquidity can cause small orders to have disproportionately large price effects.
• The theory links anomalous price impact to the square-root impact law and examines the mechanism empirically and with a numerical model.

Tags

# Anomalous price impact and the critical nature of liquidity in financial markets


# Anomalous price impact and the critical nature of liquidity in financial markets









We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the "square-root" impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.